Pith Number

pith:HCXFWPRG

pith:2013:HCXFWPRGII6DRGXBKYYANJOREJ

not attested not anchored not stored refs pending

The Embedded Transparent Lens and Fermat's Least-Time Principle

Bin Chen, Ronald Kantowski, Xinyu Dai

arxiv:1303.6648 v2 · 2013-03-26 · astro-ph.CO

Open paper page JSON Open Graph Bundle Merged state Verified badge What is a Pith Number?

Add to your LaTeX paper

\usepackage{pith}
\pithnumber{HCXFWPRGII6DRGXBKYYANJOREJ}

Prints a linked badge after your title and injects PDF metadata. Compiles on arXiv. Learn more · Embed verified badge

Record completeness

1 Bitcoin timestamp

2 Internet Archive

3 Author claim open · sign in to claim

4 Citations open

5 Replications open

✓ Portable graph bundle live · download bundle · merged state

The bundle contains the canonical record plus signed events. A mirror can host it anywhere and recompute the same current state with the deterministic merge algorithm.

Receipt and verification

First computed	2026-05-18T01:26:58.625848Z
Builder	pith-number-builder-2026-05-17-v1
Signature	Pith Ed25519 (`pith-v1-2026-05`) · public key
Schema	pith-number/v1.0

Canonical hash

38ae5b3e26423c389ae1563006a5d1226144d491e625e4a2855f30ac4f94e82e

Aliases

arxiv: 1303.6648 · arxiv_version: 1303.6648v2 · doi: 10.48550/arxiv.1303.6648 · pith_short_12: HCXFWPRGII6D · pith_short_16: HCXFWPRGII6DRGXB · pith_short_8: HCXFWPRG

Agent API

Resolver JSON Graph JSON Events JSON Schema Signing key

Verify this Pith Number yourself

curl -sH 'Accept: application/ld+json' https://pith.science/pith/HCXFWPRGII6DRGXBKYYANJOREJ \
  | jq -c '.canonical_record' \
  | python3 -c "import sys,json,hashlib; b=json.dumps(json.loads(sys.stdin.read()), sort_keys=True, separators=(',',':'), ensure_ascii=False).encode(); print(hashlib.sha256(b).hexdigest())"
# expect: 38ae5b3e26423c389ae1563006a5d1226144d491e625e4a2855f30ac4f94e82e

Canonical record JSON

{
  "metadata": {
    "abstract_canon_sha256": "c8b9a4a0643be093db1490dc48e79e7ad16ac6605b0a9f66e3c238c2469196e3",
    "cross_cats_sorted": [],
    "license": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
    "primary_cat": "astro-ph.CO",
    "submitted_at": "2013-03-26T20:07:28Z",
    "title_canon_sha256": "3c1323d9362f4a8649731a1d40da97effe2a20a982793313f6f3fc146158bc8e"
  },
  "schema_version": "1.0",
  "source": {
    "id": "1303.6648",
    "kind": "arxiv",
    "version": 2
  }
}